In order to cancel an echo signal caused by a transmitted signal and experienced by a receiver of a simultaneous transmit and receive (STR) system, one conventional approach for estimating the echo signal x(t−τ) has been to use a vector modulator having two phase shifters that arbitrarily rotates and two variable attenuators that arbitrarily scales x(t). A transmitted signal x(t) can be represented by an in-phase component and a quadrature-phase component asx(t)=xi(t)cos(ωt)+xq(t)sin(ωt)  (1)in which ω is the carrier frequency in rad/sec, xi(t) is the magnitude of the in-phase component as a function of time t, and xq(t) is the magnitude of the quadrature-phase component as a function of time t. FIG. 2 depicts an exemplary ideal estimated echo signal {tilde over (x)}(t) that has been estimated by scaling and rotating x(t) as{tilde over (x)}(t)=wix(t)+wq{circumflex over (x)}(t)  (2)in which {circumflex over (x)}(t) is the Hilbert transform of x(t) (which is a 90-degree phase shift of x(t)), and wi and wq respectively are the weights for the in-phase and quadrature-phase components of x(t). FIG. 2, in particular, depicts a vector representation of an ideal output of a conventional vector modulator.
Due to phase imbalances the phase shifters of a conventional vector modulator, however, {circumflex over (x)}(t) is typically not orthogonal to x(t). Additionally, amplitude imbalances of a conventional vector modulator cause {circumflex over (x)}(t) to typically have a different power magnitude than x(t). FIG. 3 depicts a vector representation of an exemplary output of a conventional vector modulator in which both phase and amplitude imbalances are present. As shown in FIG. 3, vector {circumflex over (x)}(t) is not orthogonal to x(t) so the vectors orthogonal to x(t) or {circumflex over (x)}(t) cannot be represented by a linear combination of x(t) and {circumflex over (x)}(t). Additionally, vector {circumflex over (x)}(t) has a different power magnitude than x(t).
It will be appreciated that for simplicity and/or clarity of illustration, elements depicted in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. The scaling of the figures does not represent precise dimensions and/or dimensional ratios of the various elements depicted herein. Further, if considered appropriate, reference numerals have been repeated among the figures to indicate corresponding and/or analogous elements.